How can I talk about the theme of family in Bud, not Buddy?
The way to develop this excellent theme in this work would be to focus on the way that Bud experiences a very bad experience of family at the start of the book. The story of the way in which Bud is tortured by Todd Amos by having a pencil shoved up his nostril when he is asleep shows the reality of Bud's life and the kind of hardships he has experienced as an orphan. We can see stemming from these experiences his profound desire to find a family, which is of course Bud's quest in the novel.
Bud has very specific memories of his mother, which have led him to form a clear view of what constitutes family in his opinion and what does not. However, during the journey that Bud makes, he experiences very different families that challenge his narrow views. For example, he meets the "fake" family who adopt him for breakfast, and then the family at Hooverville who share their meal with him. The family of Lefty Lewis take him in and feed him and clothe him. Of course Bud also enjoys having a blood brother in the form of Bugs, who is forced to leave him behind during the crush for the train at Hooverville. All of these experiences help develop the theme of family and also present the concept of family being very different from the kind of ideal that Bud has in his mind. This of course becomes particularly relevant when Bud meets his father.
The theme of family can therefore be explored through Bud's experience of very different types of family through his journey, culminating in the success of his goal, though in a very different way than he ever expected.